柔性约束下压杆的一些稳定和不稳定的临界状态

发布时间：2018-04-12 19:12

本文选题：柔性约束 + 相对刚度　；参考：《应用数学和力学》2017年08期

【摘要】：研究了一端固定、一端弹簧约束滑动固定的压杆在Euler临界载荷作用下的稳定性.将系统的势能表示为转角的泛函,将扰动量展开成Fourier级数,将势能的二阶变分表示成一个二次型,得到在临界状态下势能的二阶变分半正定,并求得临界载荷与屈曲模态.进一步研究临界状态下高阶变分的正定性,包括四阶和六阶变分的正定性.结果表明,与刚性约束不同的是,柔性约束压杆临界状态的稳定性与约束的刚度有关,有稳定与不稳定之分,并给出了临界状态是稳定和不稳定的情况下柔性约束相对刚度的范围.
[Abstract]:The stability of the compression bar with one end fixed and one end spring bound sliding fixed under the Euler critical load is studied.The potential energy of the system is expressed as a functional of the rotation angle, the perturbation quantity is expanded into a Fourier series, the second order variation of the potential energy is expressed as a quadratic form, the second order variational semidefinite of the potential energy is obtained under the critical state, and the critical loads and buckling modes are obtained.In this paper, we further study the positive definiteness of higher order variational in critical state, including the positive definiteness of fourth and sixth order variations.The results show that, unlike rigid constraints, the stability of the critical state of a flexible compression bar is related to the stiffness of the constraint, and there is a difference between stability and instability.The range of relative stiffness of flexible constraint is given when the critical state is stable and unstable.
【作者单位】：北京交通大学土木建筑工程学院力学系;
【基金】：高等学校博士学科点专项科研基金(20120009110019)
【分类号】：O342

【相似文献】